Please forgive me if this has been stickied or posted before, as I'm not too experienced with the nuts and bolts of guitars, but I'm having an issue with my Peavey T-60 electric guitar.

Basically when I play an open high e, it is in tune, but when I play at the 12th fret, it is exactly a half-step flat. Playing at the 13th fret is the octave for the high e. Also, the natural harmonic now occurs at the 13th fret instead of the 12th. Any ideas on how to rectify this problem? I tried to adjust the bridge for the high e to be closer to the fretboard, but it didn't seem to help. After tuning the string back to e after adjusting the bridge, it was still a half-step flat at the 12th fret. Maybe I'm doing something wrong?

The string saddles have screws in them so you can adjust their distances from the bridge pick-up. I did adjust the string saddle for the high E to be as close to the pickup as possible (eventually setting it so close that it popped off and I had to set it back on the string). All my other strings are perfectly in tune at the 12th fret, but yes, at the 12th fret of the high E the note is not an E but an Eb. I'm 100% positive that I'm playing the 12th fret :P

Around frets 9-11 you start to notice the notes increasing by less than half-step increments, and once you hit fret 12, it is an Eb. Fret 13 is the same note as an open high E.

As far as I can tell, the neck appears to be straight, though I'm probably not the best judge. Do you think the truss rod could be warped?

the 2 screws on the saddles adjust the hight of the individual strings and the other one thats horizontal adjust the intonation. this is likely the problem. if you loosen the screw it makes the distance between the nut and the bridge smaller. so you said you lossened it to make it closer to the bridge pick up? try tightening the saddle to make the distance longer. (i cant remember off hand what way does what to the intonation)

remember when you do it to loosen the strings when you tighten it as it will add extra tention to the string and snap it very easily.

Tuning it to a perfect E and attempting to hit the harmonic at fret 12 produces a dead note, while I can perfectly hit the harmonic at fret 13. But in response to the guy saying intonation is very, very basic, I had already tried loosing the high e string saddle before I had even posted this thread, as loose as it could go, but still had the issue. The guitar is an old Peavey T-60, and it's likely the string saddles may need to be replaced. I appreciate the help and responses!